Vectors and have magnitudes and respectively

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Vectors u\mathbf{u} and v\mathbf{v} have magnitudes 88 and 66 respectively, and the angle between them is 45∘45^\circ. Let w=2u−v\mathbf{w}=2\mathbf{u}-\mathbf{v}. The value of u⋅w\mathbf{u}\cdot\mathbf{w} is (a) 128+242128 + 24\sqrt2 (b) 64−24264 - 24\sqrt2 (c) 128−242128 - 24\sqrt2 (d) 104104

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